GRADING AND SCREENING 235 glance appear more or less cubical, scaly and longish pieces will usually be so few in comparison with the cubical shaped one that they have little or no effect on the grading work. It will be evident from what has gone before that such scaly and longish grains will in commercial work report in sizes larger than the one where they belong. In most commercial grading problems this is desirable. Material which resists crushing such as rocks and ores yield fragments which are more nearly tetrahedrons (triangular pyramids) than other shapes. The tetrahedral shape is more particularly noticeable where the rock or ore is devoid of noticeable cleavage planes. Wifch irregular shaped fragments reentering angles, protruding points and minor faces are noticeable but the four planes of a tetrahedron will be found to bound an irregular fragment more satisfactorily than a greater number. It is common to assume that rock fragments are more or less cubical but it is rara FIG. 9.—Theoretical fracture. FIG. 10.— Fragment of fractured cube. to find on them six major bounding pianos. The importance of this point will be brought out when capacities of screening machines of the flat type are discussed. If a cube of isotropic material is crushed by application of uniform pressure to two parallel faces it should break up into a series of fragments bounded by conjugate planes (Figs. 9 arid 10).l Evidently the fracturing cannot take place along the line of application nor at right angles to it and in an isotropic cube it will be at an angle of 45 deg. to the line of application of the pressure. (With cast iron the angle has been found to be 55 deg.) Since under the assumption of isotropism there can he no choice as to the number of fracture planes since all must yield simultaneously the-theoretical appearance after fracturing will be as indicated in part in Figs. 9 l"Encyclopedia Britannica," XI e4.